If you are talking the rear only, here is how it works. I am not sure about your colors. Lots of things change over the years.
1. Three wires go to rear. Rear bulbs are dual contact/dual filament. One contact for tail light filament, one contact for stop/turn filament. Each side.
2. Tail lights are wired from the headlight switch. Nothing to do with turn signal switch. One wire goes back from H/L switch and splits to each tail light filament contact and license light. That's 1 of 3.
3. One wire goes back from turn signal to left turn/stop filament contact. That's 2 of 3.
4. One wire goes back from turn signal to right turn/stop filament contact. That's 3 of 3.
5.The turn signal switch is "router". It receives a flash signal from the flasher. It receives a stop signal from brake switch. If you are in straight ahead mode and apply brakes, brake lights come on. When you move the lever to make a right turn, the T/S switch shuts off the brake signal to right and allows only a flash signal to right. Allows brake signal to left.
Same idea with left turn.
So wire it up like that and report. I don't know EXACTLY where you are testing with words like "at the cab".
It seems your truck's turn signal switch colors may be:
-light blue = to left front turn signal & dash indicator
-yellow = feed from the flasher on the fuse box
-dark blue = to right front turn signal & dash indicator
-pink = to left rear turn signal & brake contact
-violet = to right rear turn signal & brake contact
-white) = feed from brake light switch
